Flat tires are a common problem experienced by bicycle riders of all ages and experience levels. Riders are frequently in need of a pump to inflate their tires. Various wheel mounted tire pumps have been previously described and many of these pumps rely on the rotation of the tire as the source of power for the pump. For example U.S. Pat. Nos. 624,417, 652,997, 744,483, 5,342,177, 5,898,965 and 7,124,789 all describe wheel mounted tire pumps that are attached or mounted in one way or another to the wheel's axle and then extend radially away from the axle (i.e. towards the rim of the tire). These designs have a significant flaw in that they alter both the aerodynamic properties and the balance of the wheel. U.S. Pat. Nos. 2,415,618 and 5,667,606 describe automobile tire pumps that are mounted on the outside of the wheel's hub. While the pump described in the '606 patent employs movement that is substantially aligned axially to the wheel's axis, the design requires a weighted pendulum that extends downwards away from the pump. Both the '618 and '606 pumps are large and bulky and unsuitable for use with a bicycle or other light-weight vehicle, as the problems related to weight and balance and aerodynamics are only compounded by their design. Other proposed designs such as those described in U.S. Pat. Nos. 5,318,317 and 7,059,372 are similarly unwieldy.